How to prove that the equation $$x^2-3y^2=17$$ has no integer solutions? Can you help me?
2026-05-02 18:29:53.1777746593
How to prove that the equation $x^2-3y^2=17$ has no integer solutions?
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$$x^2-3y^2=17\implies x^2\equiv2\pmod 3$$
but $x$ can be $\equiv 0,\pm1\pmod 3\implies x^2\equiv0,1\pmod 3$